# Full text of "History Of The Theory Of Numbers - I"

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```SUBJECT INDEX.
Abundant, 3,7,11,14,15,20, 31-3
Agreeable, 38, 458
Algebraic numbers, 86, 221, 245, 251, 322, 379, 417, 447-8
Aliquot parts, 3, 50-8
Amantes, 39
Amiable, 38, 41
Amicable, 5, 38-50
---------of higher order, 49, 50
<--------triple, 50
Anatomiae numeronim, 348
Approximation, 114-5, 158, 281-3,318,330-1,352,354, 411, 422-3, 430, 448 (see asymptotic, mean)
Arrangement in cycles, 269
Arithmetical progression, 100-1, 114, 131, 336, (see prime)
Associated numbers, 64-6, 73
Asymptotic, 119, 122, 126-7, 129-132, 134-6, 138, 144, 154-5, 214r-5, 289, 291, 294, 301-2, 305-3, 308, 317-325, 328, 333, 416-9, 434r6, 438-440, 450 (see approximation, mean)
Aurifeuillian, 386, 390
Base, 178, 182, 186, 199, 273, 338, 340-1, 354-5, 369, 373, 375, 379, 385, 398, 454, 456, 458-460, 463-4 (see digits, periodic)
Befreundete, 38
Belongs (see exponent)
Bernoullian numbers, 100, 109, 110, 112, 140-1, 145-6, 220, 274, 278, 309, 311
Bernoulli's function, 268, 325
Bertrand's postulate, 132, 413, 425, 435-6
Bilinear form, 409
Binomial coefficients, 59, 62, 67, 77, 91, 97, 99, 266-278
--------congruence, 92-5,105,
175, 177, 204-222, 388, 391
------------------, identical, 78,
82, 87-9, 94-5
Casting out nines, 337-346
Characters, 201, 415
Circular permutations, 75,78, 81, 131, 136
Combinations, 77, 90-1, 106,
261, 281, 303, 410 Complementary fractions, 156 Congeneres, 39 Congruence (see binomial)
--------, cubic, 252-6, 262
--------, higher, 223-61
--------, identical, 73, 87-9
--------, involving  factorials,
275-8, 428
- irreducible, 84, 234-
52 --------, quartic,  254r-5, 259,
260 Congruent form, 362
-----— fractions, 258-9
--------series, 259
Conjugate functions, 444 Consecutive  numbers,   147,
332, 353, 355, 373, 457 (see
product) Continued    fractions,    138,
158, 210, 363, 367-8, 381,
393, 399, 403, 408-9 Crib (see sieve) Criteria for given divisor, 337 Cyclotomic function, 199,245,
378, 383-5, 387-90, 418
Decimal (see periodic) Defective, 3 Deficient, 3 Determinant, 77, 87, 97, 137,
149, 150-1, 226, 228, 231,
233,  261, 288,  295,   321,
336, 368, 399, 410-1, 444,
446
--------=c(modm), 155, 261
--------of Smith, 122-4, 127-
130, 136
Diatomic series, 439 Differences of order m, 62-4,
74, 78, 79, 204 ------------------two primes,
424-5
squares, 357
Digits, 81, 343, 353-4, 358, 360, 366, 438, 453-65
--------of perfect number, 7,
10, 17, 20
--------permuted in multiples, 164-5,170,174,176-7, 458-9
Digits, sum of, 263-4, 266, 272,337-8,342-3,367,455, 457-8, 461-4
Diminute, 3, 4
Equivalent fractions, 135
Euclidean number, 28
Euler's constant, 122, 134, 136, 281-3, 289, 294, 317-24, 328-30
---------criterion, 67, 205
---------generalization of Fer-
mat's theorem, 60-89, 398, 400
---------numbers, 363
--------- 0-function, 82, 85,
110, 113-58, 182, 285-6, 293, 312, 333-6, 404, 434, 441-2, 446
---------------------------1 generalized by Schemmel, 147
--------------------------Jordan,
123, 132, 147, 252, 298-9
ExcSdant, 3
Excess E of divisors 4m+1 over divisors 4m+3, 281, 289, 293, 295-6,300-1,308, 318-9
---------of odd over even
divisors, 290-1, 317-8
Exclusion method, 207, 369-70
Exponent, 61, 112, 163, 169, 181-204, 240, 242-3, 246, 257, 259, 260 (see Haupt)
---------to which 10 belongs,
159-204, 339, 341-2
---------------------------2 belongs, 111, 181,190-1,193, 198, 200, 203, 369-70
Factor tables, 347 (see graphical)
Factorial, 62-3, 77, 263-78
Factoring, 13, 25, 241, 248, 252, 357 (see graphical, criteria, sieve)
--------, number of ways of,
52, 109, 282, 285, 298, 331
Factors of 10n=*=l, 159-179 - 2n-l (see per-
fect)
381-91
bn, 258,```